This activity is meant to make students think about patterns and to figure out the rules for adding integers. They will start with an addition chart and investigate what conditions make for a positive, negative, or zero sum. I have students work in groups for this activity because I encourage the students to discuss their findings. You can use it as independent or paired practice as well. After completing this activity, there should be a whole class discussion in order to see what students found and to correct any misconceptions. It's a nice change to giving the students the rules and having them take notes. It puts the responsibility of learning onto the students.